An $su(1,1)$ algebraic approach for the relativistic Kepler-Coulomb problem

M. Salazar-Ramírez, D. Martínez, R. D. Mota, V. D. Granados

Published 2010-06-16Version 1

We apply the Schr\"odinger factorization method to the radial second-order equation for the relativistic Kepler-Coulomb problem. From these operators we construct two sets of one-variable radial operators which are realizations for the $su(1,1)$ Lie algebra. We use this algebraic structure to obtain the energy spectrum and the supersymmetric ground state for this system.